%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:39:35 PM UTC 2026
% Result : Unsatisfiable 0.16s 1.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 12 unt; 2 def)
% Number of atoms : 59 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 23 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f101,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f126,negated_conjecture,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_1) ).
fof(f127,negated_conjecture,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_2) ).
fof(f128,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_3) ).
fof(f139,plain,
( member(z,unordered_pair(x,y))
| ~ member(z,universal_class) ),
inference(superposition,[],[f10,f126]) ).
fof(f143,definition,
( spl0_1
<=> member(z,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f145,plain,
( ~ member(z,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f147,definition,
( spl0_2
<=> member(z,unordered_pair(x,y)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f149,plain,
( member(z,unordered_pair(x,y))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f150,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f139,f147,f143]) ).
fof(f167,plain,
member(z,universal_class),
inference(resolution,[],[f15,f127]) ).
fof(f168,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f167,f145]) ).
fof(f169,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f178,plain,
( x = z
| y = z
| ~ spl0_2 ),
inference(resolution,[],[f8,f149]) ).
fof(f182,plain,
( x = z
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f178,f128]) ).
fof(f183,plain,
( unordered_pair(x,y) = unordered_pair(x,x)
| ~ spl0_2 ),
inference(superposition,[],[f126,f182]) ).
fof(f185,plain,
( x != y
| ~ spl0_2 ),
inference(superposition,[],[f128,f182]) ).
fof(f192,plain,
member(y,unordered_pair(y,z)),
inference(resolution,[],[f101,f127]) ).
fof(f193,plain,
( member(y,unordered_pair(y,x))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f192,f182]) ).
fof(f194,plain,
( member(y,unordered_pair(x,y))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f193,f120]) ).
fof(f195,plain,
( member(y,unordered_pair(x,x))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f194,f183]) ).
fof(f200,plain,
( x = y
| x = y
| ~ spl0_2 ),
inference(resolution,[],[f195,f8]) ).
fof(f202,plain,
( x = y
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f200]) ).
fof(f203,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f202,f185]) ).
fof(f204,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f203]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f150]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f169]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f204]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f205,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET017-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 00:09:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.65/1.50 % (1448201)Input is clausal, will run a generic CNF schedule.
% 3.65/1.50 % (1448207)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2975518935:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.65/1.50 % (1448210)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1651348500:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.65/1.50 % (1448206)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2482478404:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.65/1.50 % (1448211)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2489618253:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.65/1.50 % (1448212)dis-21_1_sil=8000:lcm=predicate:random_seed=3976498879:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.65/1.50 % (1448209)lrs+10_1_sil=8000:sp=occurrence:random_seed=2674278164:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.65/1.50 % (1448208)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3114264847:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.65/1.50 % (1448209)First to succeed.
% 3.65/1.50 % (1448209)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1448201"
% 3.65/1.50 % (1448210)Also succeeded, but the first one will report.
% 3.65/1.50 % (1448211)Also succeeded, but the first one will report.
% 3.65/1.50 % (1448212)Instruction limit reached!
% 3.65/1.50 % (1448212)------------------------------
% 3.65/1.50 % (1448212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.50 % (1448212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.50 % (1448212)CaDiCaL version: 2.1.3
% 3.65/1.50 % (1448212)Termination reason: Instruction limit
% 3.65/1.50 % (1448212)Termination phase: Saturation
% 3.65/1.50 % (1448212)Time elapsed: 0.077 s
% 3.65/1.50 % (1448212)Peak memory usage: 88 MB
% 3.65/1.50 % (1448212)Instructions burned: 117 (million)
% 3.65/1.50 % (1448220)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=4141910379:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.16/1.50 % (1448209)Refutation found. Thanks to Tanya!
% 0.16/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.50 % (1448209)------------------------------
% 0.16/1.50 % (1448209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.50 % (1448209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.50 % (1448209)CaDiCaL version: 2.1.3
% 0.16/1.50 % (1448209)Termination reason: Refutation
% 0.16/1.50 % (1448209)Time elapsed: 0.005 s
% 0.16/1.50 % (1448209)Peak memory usage: 89 MB
% 0.16/1.50 % (1448209)Instructions burned: 4 (million)
% 0.16/1.50 % (1448209)------------------------------
% 0.16/1.50 % (1448209)------------------------------
% 0.16/1.50 % (1448201)Success in time 0.439 s
% 0.16/1.50 % Vampire exiting
%------------------------------------------------------------------------------